Pith Number

pith:PHYB4INC

pith:2014:PHYB4INCRFYXT34IYZQZF6HCNE

not attested not anchored not stored refs pending

Stochastic differential equation with jumps for multi-type continuous state and continuous time branching processes with immigration

Gyula Pap, Matyas Barczy, Zenghu Li

arxiv:1403.0245 v2 · 2014-03-02 · math.PR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PHYB4INCRFYXT34IYZQZF6HCNE}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T01:10:41.473241Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

79f01e21a2897179ef88c66192f8e269346b63d5bd4c32baeef329d737c1da56

Aliases

arxiv: 1403.0245 · arxiv_version: 1403.0245v2 · doi: 10.48550/arxiv.1403.0245 · pith_short_12: PHYB4INCRFYX · pith_short_16: PHYB4INCRFYXT34I · pith_short_8: PHYB4INC

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/PHYB4INCRFYXT34IYZQZF6HCNE \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 79f01e21a2897179ef88c66192f8e269346b63d5bd4c32baeef329d737c1da56

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "efdee24800e39d9a53f0d87e447c37cc2f7da85e5e89a7bc99ca5a6cf8617590",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2014-03-02T17:31:01Z",
    "title_canon_sha256": "31cb917f8f8884a079c3dce6472a2ff3c7422b2164e19ce9145b849723fb4fd1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1403.0245",
    "kind": "arxiv",
    "version": 2
  }
}